Question

In a Young’s double slit experiment, 12 fringes are observed to be formed in a certain region of the screen when light of wavelength 600 nm is used. If the light of wavelength 400 nm is used, the number of fringes observed in the same region of the screen will be:

• A. 12
• B. 18
• C. 24
• D. 8

Answer 1

The correct option is B 18

Fringe width $f_1=\frac{{\lambda }_{1}D}{d}$
region of screen $x=12\times f_1$
As D and d remain the same.
region of screen $x=$ number of fringes $\times f_2$
$f_2=\frac{{\lambda }_{2}D}{d}$
$12\times f_1=$ number of fringes $\times f_2$
$12\times {\lambda }_1=$ number of fringes $\times {\lambda }_2$
Number of fringes $=12\times \frac{{\lambda }_1}{{\lambda }_2}$ $=12\times \frac{600}{400}=18$